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Register a new userRepulsive Casimir forces with finite-thickness slabs
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We use the extended Lifshitz theory to study the behaviors of the Casimir forces between finite-thickness effective medium slabs. We first study the interaction between a semi-infinite Drude metal and a finite-thickness magnetic slab with or without substrate. For no substrate, the large distance $d$ dependence of the force is repulsive and goes as $1/d^5$; for the Drude metal substrate, a stable equilibrium point appears at an intermediate distance which can be tuned by the thickness of the slab. We then study the interaction between two identical chiral metamaterial slabs with and without substrate. For no substrate, the finite thickness of the slabs $D$ does not influence significantly the repulsive character of the force at short distances, while the attractive character at large distances becomes weaker and behaves as $1/d^6$; for the Drude metal substrate, the finite thickness of the slabs $D$ does not influence the repulsive force too much at short distances until $D=0.05lambda_0$.
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Both theoretical interest and practical significance attach to the sign and strength of Casimir forces. A famous, discouraging no-go theorem states that The Casimir force between two bodies with reflection symmetry is always attractive. Here we identify a loophole in the reasoning, and propose a universal way to realize repulsive Casimir forces. We show that the sign and strength of Casimir forces can be adjusted by inserting optically active or gyrotropic media between bodies, and modulated by external fields.
Casimir and Casimir-Polder repulsion have been known for more than 50 years. The general Lifshitz configuration of parallel semi-infinite dielectric slabs permits repulsion if they are separated by a dielectric fluid that has a value of permittivity that is intermediate between those of the dielectric slabs. This was indirectly confirmed in the 1970s, and more directly by Capassos group recently. It has also been known for many years that electrically and magnetically polarizable bodies can experience a repulsive quantum vacuum force. More amenable to practical application are situations where repulsion could be achieved between ordinary conducting and dielectric bodies in vacuum. The status of the field of Casimir repulsion with emphasis on recent developments will be surveyed. Here, stress will be placed on analytic developments, especially of Casimir-Polder (CP) interactions between anisotropically polarizable atoms, and CP interactions between anisotropic atoms and bodies that also exhibit anisotropy, either because of anisotropic constituents, or because of geometry. Repulsion occurs for wedge-shaped and cylindrical conductors, provided the geometry is sufficiently asymmetric, that is, either the wedge is sufficiently sharp or the atom is sufficiently far from the cylinder.
In our previous work [Phys. Rev. Lett. 103, 103602 (2009)], we found that repulsive Casimir forces could be realized by using chiral metamaterials if the chirality is strong enough. In this work, we check four different chiral metamaterial designs (i.e., Twisted-Rosettes, Twisted-Crosswires, Four-U-SRRs, and Conjugate-Swastikas) and find that the designs of Four-U-SRRs and Conjugate-Swastikas are the most promising candidates to realize repulsive Casimir force because of their large chirality and the small ratio of structure length scale to resonance wavelength.
Electromagnetism in substance is characterized by permittivity (dielectric constant) and permeability (magnetic permeability). They describe the substance property {it effectively}. We present a {it geometric} approach to it. Some models are presented, where the two quantities are geometrically defined. Fluctuation due to the micro dynamics (such as dipole-dipole interaction) is taken into account by the (generalized) path-integral. Free energy formula (Lifshitz 1954), for the material composed of three regions with different permittivities, is explained. Casimir energy is obtained by a new regularization using the path-integral. Attractive force or repulsive one is determined by the sign of the {it renormalization-group} $beta$-function.
We investigate repulsive Casimir force between slabs containing left-handed materials with controllable electromagnetic properties. The sign of Casimir force is determined by the electric and magnetic properties of the materials, and it is shown that the formation of the repulsive force is related to the wave impedances of two slabs. The sign change of the Casimir force as a function of the distance is studied. Special emphasis is put on the restoring Casimir force which may be found to exist between perfectly conducting material and metamaterial slabs. This restoring force is a natural power for the system oscillation in vacuum and also can be used for system stabilization.
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